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We investigate the optimal measurement strategy for state discrimination ofthe trine ensemble of qubit states prepared with arbitrary prior probabilities.Our approach generates the minimum achievable probability of error and also themaximum confidence strategy. Although various cases with symmetry have beenconsidered and solution techniques put forward in the literature, to ourknowledge this is only the second such closed form, analytical, arbitraryprior, example available for the minimum-error figure of merit, after thesimplest and well-known two-state example.

Optimal measurement strategies for the trine states with arbitrary prior probabilities